Accurate characterization of pore size and pore-size distribution is essential for the semi-permeable membranes that are used for applications such as water desalination, industrial gas separations, renal dialysis, membrane lung oxygenators, controlled-release drug delivery devices, and membrane-based sensors. In these applications the pore size determines the ability of the membrane to retain larger particles, bacteria, macromolecules, molecular aggregates, or molecules relative to the liquid or gas that permeates through the membrane. Such characterization is also required for porous electrodes used in batteries and fuel cells where the pore size determines the available surface area for charge transfer as well as for porous catalysts used in a variety of chemical processes where the pore size determines the available surface area for the heterogeneous catalytic reaction.
Several methods of characterizing the membrane pore-size distribution exist, and many have been well-reviewed. However, each technique is applicable to only a relatively limited range of pore sizes. For example, one can indirectly determine the pore-size distribution of a membrane by examining its rejection characteristics. Unfortunately, the solution for the pore-size distribution from sieving data is mathematically ill-posed without a unique solution. Gamma, lognormal, normal and Weibel-Rayleigh distribution functions have been used to fit the pore-size distribution data obtained from solute rejection, and observed that the area-averaged sieving coefficients are sensitive to the choice of the probability distribution functions. This could lead to uncertainty in the pore-size distribution obtained.
Microscopy techniques based on scanning electron microscopy (SEM), field-emission scanning electron microscopy (FESEM), and atomic force microscopy (AFM) have also been used to characterize pore structure. Microscopy techniques require expensive instruments that can measure only the pore size within a planar surface for a sample area of only a few hundred micrometers. As such, microscopy does not characterize the pore size throughout a porous sample of interest but rather provides a two-dimensional measure of a three-dimensional characteristic. Nonetheless, pore-size analysis based on microscopy provides important information regarding the pore-geometry, surface properties and anisotropy, which often play a major role in separation.
SEM requires skillful sample preparation to minimize artifacts due to drying and freeze-fracture that can often modify the original morphology and present a distorted presentation of the actual membrane structure. The use of AFM on membranes may cause the surface of the membrane to be distorted due to tip convolution. If the changes of height on the surface are of sufficient magnitude (>5 μm), contact may be lost between the tips and the sample. There is also often a discrepancy between pore sizes observed by microscopy and manufacturer-supplied pore-size ratings, mainly because the former is a direct measure of the pores on the membrane surface while the manufacturers report the size of particles retained by the membrane.
Mercury intrusion porosimetry measures the pressure required to force mercury into membrane pores. Both the volumes of through and blind pores are measured. However, this involves the use of high pressures with a toxic substance.
In capillary flow porometry (CAP), a non-reacting gas is passed through a dry sample, and then through the same sample after it has been wetted with a liquid. Based on the surface tension of the liquid and the difference in the pressures required, the size of the smallest neck in each pore can be determined. CAP measures the pore-throat diameter only, and does not give an indication of the pore volume.
U.S. Pat. No. 5,002,399 to Akinic describes another temperature-based technique for determining a material's porosity characteristics. In this technique, the porous material is saturated with a liquid, placed within an enclosed area, and then progressively heated by a furnace. As the temperature increases, the wetting liquid evaporates first from large diameter pores then from small diameter pores. The technique requires that both the temperature and mass of the material may be measured, and porosity is determined by measuring the change in mass as a function of temperature. In order to evaporate the liquid from pores with nm radii requires heating the material to temperatures exceeding 300° C. In addition to requiring a testing device that must accurately measure both temperature and mass within a closed environment, the high temperatures necessitated by this technique may alter the pore structure and/or degrade the porous material, thus, greatly limiting the types of membranes that can be tested.
Liquid displacement porometry (LDP) involves saturating the membrane with a wetting liquid and then gradually increasing the pressure of an immiscible fluid to cause displacement of the liquid progressively from the largest to the smallest pores as dictated by the Young-Laplace equation that relates the pore diameter to the pressure differential. The volume of pores of a given diameter can be determined from the flow rate if a model is assumed for the flow geometry. However, LDP is limited for characterizing ultra-filtration (UF) membranes owing to the high pressures required. For example, a UF membrane with a nominal pore size of 20 nm requires a pressure differential of 3.4 MPa to displace a wetting liquid having a surface tension of 15.9 mN/m. High pressures can cause compaction, thereby altering the membrane morphology.
Another pore-size characterization method for UF membranes is gas adsorption/desorption (GAD), which involves filling the pores via adsorption and capillary condensation by increasing the pressure of a gas. The pressure is then reduced to cause desorption of the liquid progressively from the largest to the smallest pores as dictated by the Kelvin equation that relates the pore diameter to the vapor pressure depression. The volume of pores of a given diameter can be determined from the volume of gas desorbed. GAD encounters limitations for larger pores owing to their smaller vapor-pressure reduction and limited accuracy in measuring the pressure and volume.
Thermoporometry involves freezing a liquid-saturated membrane and then gradually increasing the temperature to cause melting progressively from the largest to the smallest pores as dictated by the Gibbs-Thompson equation that relates the pore diameter to the freezing-point depression. The volume of pores of a given diameter is determined from the differential heat input. However, measuring this heat input with sufficient accuracy limits thermoporometry. In addition, a correction is required for the smallest pores owing to a submicron layer of unfrozen liquid at the pore walls that is caused by disjoining pressure effects.
Permporometry (PP) is a variation of GAD that involves simultaneous flow of a non-condensable gas that permits measuring only the continuous pores to the exclusion of the dead-end pores. PP is based upon filling the entire pore structure with a condensable gas, and subsequently removing this gas by progressively lowering its partial pressure. As the pressure is reduced, pores having a size corresponding to the vapor pressure applied are emptied, and become available for gas transport. The vapor pressure is related to the pore size by the Kelvin equation. Maintaining equal pressures on both sizes of the membrane to avoid pressure-driven flow during desorption is difficult, and a correction must be made to the data to account for the adsorbed monolayer that remains in each pore after desorption. PP is subject to the same limitations as GAD. Moreover, the required control of the gas partial pressure is difficult.
Ultrasonic reflectometry has demonstrated significant capability as a real-time, non-destructive and non-invasive tool for characterizing various membrane processes. Ultrasonic spectroscopy using highly sensitive piezoelectric transducers has been employed to study the acoustic properties of polymer membranes and relate them to their filtration characteristics. General trends between velocity and membrane properties have been described, as well as relationships between the acoustic properties to actual pore characteristics. The application of ultrasonic reflectometry has been broadened to accommodate the non-invasive characterization of membrane morphology including defect detection. However, pore-size determination in this case does not represent a primary measurement, but rather reflects a statistical fit to a known distribution.
Overall, there is no one technique that is capable of determining pore sizes ranging from nanometer to the micrometer scale, the range of interest in membrane applications. Techniques such as DP require relatively expensive dedicated equipment that involves the application of high pressures that can deform the material being studied. Moreover, DP can characterize only relatively large pores that are typically larger than 10 nm. Techniques such as gas adsorption/desorption also require relatively expensive dedicated equipment that involves measuring the gas pressure very accurately. Moreover, gas adsorption/desorption relies on a phenomenon known as capillary condensation whereby pores fill by progressive adsorption. For this reason, gas adsorption/desorption can accurately characterize only relatively small pores, i.e., typically less than 10 nm. Techniques such as SEM and AFM require expensive instrumentation that can measure only the pore size within a planar surface for a sample area of only a few hundred micrometers. As such, microscopy does not characterize the pore size throughout a porous sample of interest. Other less commonly used pore-size characterization techniques such as TP and PP also require dedicated relatively expensive equipment and are difficult to implement reliably.
The information included in this Background section of the specification, including any references cited herein and any description or discussion thereof, is included for technical reference purposes only and is not to be regarded subject matter by which the scope of the invention is to be bound.